Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+5y &= 1 \\ 3x+5y &= -5\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = -5y-5$ Divide both sides by $3$ to isolate $x$ $x = {-\dfrac{5}{3}y - \dfrac{5}{3}}$ Substitute this expression for $x$ in the first equation. $6({-\dfrac{5}{3}y - \dfrac{5}{3}}) + 5y = 1$ $-10y - 10 + 5y = 1$ Simplify by combining terms, then solve for $y$ $-5y - 10 = 1$ $-5y = 11$ $y = -\dfrac{11}{5}$ Substitute $-\dfrac{11}{5}$ for $y$ in the top equation. $6x+5( -\dfrac{11}{5}) = 1$ $6x-11 = 1$ $6x = 12$ $x = 2$ The solution is $\enspace x = 2, \enspace y = -\dfrac{11}{5}$.